The generator matrix

 1  0  1  1  2  1  1  1 X+2  1  1 2X+2  X  1  1  1  1  0 2X  1  1 3X+2  1  1 3X  X  1  1  X  1  1  1 3X+2  1  1  2  1  1  1 2X  1  1  1 2X+2  1 3X+2  1  1  1  1  1  1  0  1 X+2  1  1  1  1  1  1  1 2X 3X  1  1 3X  1  1  1 X+2  2  1  1 2X+2  1  1  1  1 2X+2 2X+2  X 3X+2  1  1  1  1  1 2X 2X
 0  1  1 X+2  1 X+3  2  3  1 X+1  X  1  1  0  3 2X+2 2X+1  1  1  X X+3  1 3X+2 3X+1  1  1  2  1  1  0  3 3X  1  2 2X+3  1  3 3X  2  1 3X+3 3X+2  3  1 3X+1  1  X 3X+3 3X+1  1 3X+3  1 2X  0  1 3X+1 3X+1  3 3X+3 3X+3 3X+3  1  1  1 3X+1  1  1 2X+2 X+2  X  1  1 3X+3  0 2X  1  3 X+3 3X+2  1  1  1  1 X+2  0 3X+3 2X+3 2X+1  1  1
 0  0  X  0 3X  X 3X 2X  0 2X 3X 3X+2  2 2X+2 2X+2 3X+2 3X+2 X+2 3X 3X+2 3X+2 2X+2 2X+2 2X+2  0  X  2  2 3X+2 X+2 X+2 2X  X  0  X 2X+2 X+2 X+2 3X 2X+2 2X 3X  0 2X 2X+2 X+2 2X+2  X  X 3X X+2  0  X 3X 2X  0 3X+2  2  2 X+2 2X+2 2X  0 2X+2 3X+2 3X+2 3X+2  0  X  2 3X+2 2X+2 3X+2 X+2  X  0  X 3X 2X  X 3X 3X  X X+2 2X+2  0 2X 2X+2  2  2
 0  0  0 2X  0 2X 2X 2X 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X  0 2X  0  0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0 2X  0  0 2X 2X  0 2X 2X  0  0 2X  0 2X  0  0 2X 2X  0 2X  0  0 2X 2X 2X  0 2X  0 2X 2X  0  0  0 2X 2X  0  0 2X  0 2X 2X  0  0 2X 2X 2X  0 2X 2X  0 2X 2X 2X  0

generates a code of length 90 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+651x^86+1074x^88+985x^90+708x^92+473x^94+134x^96+39x^98+28x^102+1x^104+1x^120+1x^128

The gray image is a code over GF(2) with n=720, k=12 and d=344.
This code was found by Heurico 1.16 in 142 seconds.